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We present an exploratory calculation of the I = 2 scattering amplitude at threshold using Wilson fermions in the quenched approximation, including all the required contractions. We nd good agreement with the predictions of chiral perturbation theory even for pions of mass 560-700 MeV. Within the 10% errors, we do not see the onset of the bad chiral behavior expected for Wilson fermions. We also derive rigorous inequalities that apply to 2-particle correlators and as a consequence show that the interaction in the antisymmetric state of two pions has to be attractive.

We calculate the perturbative corrections to fermion bilinears that are used in numerical simulations when extracting weak matrix elements using staggered fermions. This extends previous calculations of Golterman and Smit, and Daniel and Sheard. In particular, we calculate the corrections for non-local bilinears defined in Landau gauge with gauge links excluded. We do this for the simplest operators, i.e. those defined on a 2 4 hypercube, and for tree level improved operators which live on 4 4 hypercubes. We also consider gauge invariant operators in which the "tadpole" contributions are suppressed by projecting the sums of products of gauge links back in to the gauge group. In all cases, we find that the variation in the size of the perturbative corrections is smaller than those with the gauge invariant unimproved operators. This is most strikingly true for the smeared operators. We investigate the efficacy of the mean-field method of Lepage and Mackenzie at summing up tadpole contributions. In a companion paper we apply these results to four-fermion operators.

We present results for one-loop matching coefficients between continuum fourfermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark lines, and "penguin" diagrams containing quark loops. For the former we use Landau gauge operators, with and without O(a) improvement, and including the tadpole improvement suggested by Lepage and Mackenzie. For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for KK mixing and K → ππ decays with all corrections of O(g 2 ) included. We also discuss the mixing of ∆S = 1 operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction.

(To be submitted to Nucl. Instr. Meth. A) described. electrons, muons, neutrinos (from missing energy), charged hadrons, ·rr°'s and V°'s is of the detector is its ability to identify particles; the performance in identification of hadrons, and the accuracy obtained in energy and angle is given. An essential property of charged tracks is specified. Calorimeters are used to measure photons and neutral accuracy of the tracking detectors to measure the impact parameter and momentumThe performance of the ALEPH detector at the LEP e+e' collider is reviewed. The Abstract The ALEPH Collaboration" Performance of the ALEPH detector at LEP